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We use the extended Press–Schechter (EPS) formalism to study halo assembly histories in a standard Λ cold dark matter cosmology. A large ensemble of Monte Carlo random walks provides the entire halo membership histories of a representative set of dark matter particles, which we assume to be neutralinos. The first-generation haloes of most particles do not have a mass similar to the free-streaming cut-off Mfs of the neutralino power spectrum, nor do they form at high redshift. Median values are M1= 105–107Mfs and z1= 13 to 8 depending on the form of the collapse barrier assumed in the EPS...

We use the extended Press–Schechter (EPS) formalism to study halo assembly histories in a standard Λ cold dark matter cosmology. A large ensemble of Monte Carlo random walks provides the entire halo membership histories of a representative set of dark matter particles, which we assume to be neutralinos. The first-generation haloes of most particles do not have a mass similar to the free-streaming cut-off Mfs of the neutralino power spectrum, nor do they form at high redshift. Median values are M1= 105–107Mfs and z1= 13 to 8 depending on the form of the collapse barrier assumed in the EPS model. For almost one third of all particles, the first-generation halo has M1 > 109Mfs. At redshifts beyond 20, most neutralinos are not yet part of any halo but are still diffuse. These numbers apply with little modification to the neutralinos which are today part of haloes similar to that of the Milky Way. Up to 10 per cent of the particles in such haloes were never part of a smaller object; the typical particle has undergone approximately five ‘accretion events’ where the halo it was part of falls into a more massive object. Available N-body simulations agree well with the EPS predictions for an ‘ellipsoidal’ collapse barrier, so these may provide a reliable extension of simulation results to smaller scales. The late formation times and large masses of the first-generation haloes of most neutralinos suggest that they will be disrupted with high efficiency during halo assembly.